Learn Turkish: Kadın telefonda bir numara çeviriyordu. - The woman was dialing a number on the phone.

This uses the past continuous tense, which expresses what someone was doing. You take the verb root çevir-, add the present continuous suffix -iyor to get çeviriyor (is dialing), and then attach the past tense suffix -du to get çeviriyordu (was dialing). Because the subject is kadın (she/third-person singular), we don't need to add any personal pronoun suffix at the end.

I thought çevirmek meant "to turn". Why does it mean "to dial" here?

The core meaning of çevirmek is indeed "to turn". Before smartphones and push-buttons, people used rotary phones where you literally had to turn a circular dial to make a call. The phrase numara çevirmek (to dial a number) has survived into the modern era!

Why is the locative case -da used in telefonda if the English translation is "on the phone"?

English uses the preposition "on" for phones, computers, and TV. Turkish generally uses the locative case suffix -da or -de (meaning "in" or "at") when referring to being on a device or medium. So telefonda is how you say "on the phone".

Why isn't the accusative case used for the number (numarayı)?